Abstract

The unexpected fact that a spherical dielectric particle with refractive index higher than the surrounding medium will not always be attracted towards high intensity regions of the trapping beam is fully demonstrated here using a simple ray optics approach. This unusual situation may happen due to the inversion of gradient forces, as shown here. Therefore, conventional schemes, such the one based on the use of two counter-propagating beams to cancel the scattering forces, will fail to trap the particle. However, effective trapping still can be obtained by adopting suitable incident laser beams.

Figures (6)

(a). Ray optics analysis showing an incident ray R1 and its first two refracted rays R2 and R3. Looking at the momentum transfer without considering the infinite series of refracted/reflected rays which appears as a consequence of R1 leads to an erroneous interpretation and to the conclusion that the particle would experience a force directed to the high intensity region, i.e., to the centre of the beam. (b). the complete picture taking into account the infinite series of refracted/reflected rays.

Reflectivity for nm = 1.33 and np = 1.6, 2.4, 3.2 and 4.0 for (a) perpendicular polarization and (b) parallel polarization. If the laser is designed for case (b), then the incident rays can be chosen so that only the contribution of those with incidence angles close to regions of low reflectivity are relevant.

Gradient (a) and scattering (b) total forces for a circularly polarized TEM00 Gaussian beam as functions of the distance r between the centre of the particle and the beam focus when both are on a horizontal plane perpendicular to the optical axis of the beam. The attractive/repulsive pattern depends on the value of the refractive index np for a fixed nm.

(a). Coordinate system for total force numerical calculations. (b) Scattering factor QS and (c) gradient factor Qg as functions of the angle γ between the optical axis of the beam and the vector connecting its focus to the centre of the particle. Higher repulsive scattering total forces are seen as np increases, whereas the gradient total forces become repulsive.

Gradient total forces profile for a particle in a zero-order Bessel beam with λ = 1064 nm and a spot of 28.89 μm. The particle has a radius of a = 10.64 μm. For np = 8.0, points at r/a = 2.8 and 6.3 become points of stable equilibrium, and the use of two counter propagating Bessel beams present themselves as excellent alternatives for trapping these high refractive index particles.